Definition 4 [1]}
For a hypothesis space \(\mathcal {H}\) , the \(\mathcal {H}\Delta \mathcal {H}\) -distance between two distributions \(\mathcal {D}_1\)  and \(\mathcal {D}_2\)  is defined as
\(d_{\mathcal {H} \Delta \mathcal {H}}(\mathcal {D}_1,\mathcal {D}_2) = \sup _{h,h^{\prime }\in \mathcal {H}}\left|\text{Pr}_{\mathbf {x}\sim \mathcal {D}_1}(h(\mathbf {x})\ne h^{\prime }(\mathbf {x})) - \text{Pr}_{\mathbf {x}\sim \mathcal {D}_2}(h(\mathbf {x})\ne h^{\prime }(\mathbf {x})) \right|.\) 

